Kasturi Sunanda

Kasturi Sunanda

Answered question

2022-07-31

Answer & Explanation

alenahelenash

alenahelenash

Expert2023-06-19Added 556 answers

To solve this problem, we will use the principles of rotational motion and friction. Let's break down the given information step by step.
We are given:
- Radius of the wheel, r=0.5m
- Moment of inertia of the wheel, I=10kg·m2
- Angular speed of the wheel, ω=70rev/min
- Time taken to stop the wheel, t=5.0s
- Radially inward force applied, F=88N
First, let's convert the angular speed from revolutions per minute to radians per second. We know that 1rev=2πrad, and there are 60s in a minute:
ω=(70rev/min)·(2πrad1rev)·(1min60s)
Simplifying the conversion, we get:
ω=7π3rad/s
Next, we can calculate the initial angular momentum of the wheel. The formula for angular momentum is L=Iω:
L=(10kg·m2)·(7π3rad/s)
Simplifying the calculation:
L=70π3kg·m2·s1
To stop the wheel, a radially inward force is applied. This force is the result of the friction between the wheel and the wet cloth. The torque generated by this force causes the angular momentum to change. The formula for torque is τ=Iα, where α is the angular acceleration.
The angular acceleration can be calculated as the change in angular speed divided by the time taken:
α=ΔωΔt=07π35.0s
Simplifying further:
α=7π15rad/s2
Now, we can determine the torque generated by the friction force. The formula for torque is τ=Fr, where r is the radius of the wheel:
τ=(88N)·(0.5m)
τ=44Nm
Since torque is equal to Iα, we can equate the two:
44Nm=(10kg·m2)·(7π15rad/s2)
Simplifying the equation:
154π15=7π3·1015
Solving for π, we find:
π=3
Therefore, the coefficient of kinetic friction between the wheel and the wet cloth is π=3.
The solution is represented as:
The coefficient of kinetic friction between the wheel and the wet cloth is π=3.

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